Geodesic
Dirichlet Problem for a Class of Quasilinear Elliptic Equations
Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 592-603.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, the Dirichlet problem for quasilinear elliptic equations is studied. New a priori estimates of the solution and its gradient are obtained. These estimates are derived without any assumptions on the smoothness of the coefficients and the right-hand side of the equation. Moreover, an arbitrary growth of the right-hand side with respect to the gradient of the solution is assumed. On the basis of the resulting estimates, existence theorems are proved. 
@article{MZM_2004_76_4_a10,
     author = {A. S. Tersenov},
     title = {Dirichlet {Problem} for a {Class} of {Quasilinear} {Elliptic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {592--603},
     publisher = {mathdoc},
     volume = {76},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a10/}
}
TY  - JOUR
AU  - A. S. Tersenov
TI  - Dirichlet Problem for a Class of Quasilinear Elliptic Equations
JO  - Matematičeskie zametki
PY  - 2004
SP  - 592
EP  - 603
VL  - 76
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a10/
LA  - ru
ID  - MZM_2004_76_4_a10
ER  - 
%0 Journal Article
%A A. S. Tersenov
%T Dirichlet Problem for a Class of Quasilinear Elliptic Equations
%J Matematičeskie zametki
%D 2004
%P 592-603
%V 76
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a10/
%G ru
%F MZM_2004_76_4_a10
A. S. Tersenov. Dirichlet Problem for a Class of Quasilinear Elliptic Equations. Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 592-603. http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a10/

[1] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973

[2] Gilbarg D., Trudinger N. S., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | Zbl

[3] Krylov N. V., Nelineinye ellipticheskie i parabolicheskie uravneniya vtorogo poryadka, Nauka, M., 1985

[4] Bernshtein S. N., Ob uravneniyakh variatsionnogo ischisleniya, Sobr. sochinenii, Izd-vo AN SSSR, M., 1960

[5] Amman H., Crandall M. G., “On some existence theorems for semi-linear elliptic equations”, Indiana Univ. Math. J., 27:5 (1978), 779–790 | DOI | MR

[6] Pokhozhaev S. I., “Ob uravneniyakh vida $\Delta u=f(x,u,Du)$”, Matem. sb., 113(155):2(10) (1980), 324–338 | MR | Zbl

[7] Tersenov Al. S., “Estimate of the solution of the Dirichlet problem for parabolic equations and applications”, J. Math. Anal. Appl., 273:1 (2002), 206–216 | DOI | MR

[8] Kruzhkov S. N., “Kvazilineinye parabolicheskie uravneniya i sistemy s dvumya nezavisimymi peremennymi”, Tr. sem. im. I. G. Petrovskogo, no. 5, Izd-vo Mosk. un-ta, M., 1979, 217–271 | MR

[9] Kamynin V. L., “Apriornye otsenki i globalnaya razreshimost kvazilineinykh parabolicheskikh uravnenii”, Vestn. MGU. Ser. 1. Matem., mekh., 1981, no. 1, 33–38 | MR | Zbl

[10] Kamynin V. L., “Apriornye otsenki reshenii kvazilineinykh parabolicheskikh uravnenii na ploskosti i ikh prilozheniya”, Differents. uravneniya, 19:5 (1983), 590–598 | MR | Zbl

[11] Khusnutdinova N. V., “Ob usloviyakh ogranichennosti gradienta resheniya vyrozhdayuschikhsya parabolicheskikh uravnenii”, Dinamika sploshnoi sredy, 71 (1985), 120–129 | MR

[12] Tersenov Al. S., “On quasilinear non-uniformly elliptic equations in some non-convex domains”, Comm. Partial Differential Equations, 23:11 (1998), 2165–2186 | DOI | MR

[13] Tersenov Al. S., “On quasilinear non-uniformly parabolic equations in general form”, J. Differential Equations, 142:1 (1998), 263–276 | DOI | MR | Zbl

[14] Tersenov Al. S., Tersenov Ar. S., “The Cauchy problem for a class of quasilinear parabolic equations”, Ann. Mat. Pura Appl., 182:3 (2003), 325–336 | DOI | MR